Method for the temperature-compensated, electro-optical measurement of an electrical voltage and device for carrying out the method

ABSTRACT

In order to measure an electrical voltage in an electrooptical voltage converter, polarized light at two wavelengths is sent through the medium ( 1 ). On the output side, the light is passed through a polarizer ( 10 ) and the remaining signal is measured. In order to compensate for the temperature dependency of the electrooptical coefficients, the measurement results at the two wavelengths are compared with one another, and that voltage value which is consistent with both measurements is used.

DESCRIPTION

[0001] 1. Technical Field

[0002] The invention relates to a method for measurement of an electrical voltage using an electrooptical medium as claimed in the precharacterizing clause of claim 1, and to an apparatus for measurement of an electrical voltage as claimed in the precharacterizing clause of claim 8.

[0003] 2. Prior Art

[0004] An electrooptical medium is a material whose refractive index and in which the speed of which light propagates vary for at least one light polarization when an electric field is applied.

[0005] The measurement of electrical voltages by means of electrooptical media is known. A corresponding appliance is disclosed, for example, in U.S. Pat. No. 4,904,931. This contains an electrooptical crystal between two polarizers. The Pockel effect causes a change in the refractive index in the crystal, and this leads to the light intensity being modulated after the second polarizer. This modulation is periodically dependent on the voltage. In order to obtain a unique measurement result, two beams at the same wavelength are therefore passed through the crystal in U.S. Pat. No. 4,904,931.

[0006] U.S. Pat. No. 4,531,092 discloses a method for measurement of an electrical voltage, in which two beams at different wavelengths are sent through an electrooptical crystal. In the process, only one of the two beams is polarized on the outside, so that the intensity of the second beam is not dependent on the voltage. This measure allows the second beam to be used as a reference variable, and allows the accuracy of the measurement to be improved.

[0007] The method which is disclosed in the cited U.S. Pat. No. 4,531,092 forms the precharacterizing clause of claim 1, and the apparatus which is described therein forms the precharacterizing clause of claim 8.

[0008] For methods of the type mentioned above, the effective electrooptical coefficient must be known accurately. Since this coefficient is generally dependent on the temperature, this can lead to inaccuracies.

DESCRIPTION OF THE INVENTION

[0009] The invention is based on the object of providing a method of the type mentioned initially and the corresponding apparatus, by means of which it is possible to compensate for temperature-dependent fluctuations in a simple manner.

[0010] This object is achieved by the method as claimed in claim 1 and by the apparatus as claimed in claim 8.

[0011] According to the invention, two light beams at different wavelengths thus pass through the electrooptical medium, with the signals A₁, A₂ in the two light beams being measured after the output polarizer. These signals A₁, and A₂ are functions f₁ and f₂ of the electrical voltage V that is to be measured, and of the temperature T. According to the invention, a search is carried out for those values of the temperature T and of the voltage V which solve the equation system

A ₁ =f ₁(T, V) and

A ₂ =f ₂(T, V)

[0012] The additional information which results from the measurement at a second wavelength is thus used for determination of T and thus for elimination of the temperature dependency.

[0013] The apparatus according to the invention has an analyzer (polarizer), which polarizes a second of the two light beams, as well as a means for determination of those values of the temperature T and of the electrical voltage V, which solve the above equation system.

BRIEF DESCRIPTION OF THE DRAWING

[0014] Further refinements, advantages and applications of the invention result from the dependent claims and from the description which now follows, with reference to the FIGURE, in which:

[0015]FIG. 1 shows a schematic illustration of a voltage converter that is suitable for carrying out the invention.

WAYS TO IMPLEMENT THE INVENTION

[0016]FIG. 1 shows a schematic illustration of a cuboid BGO crystal 1, which is provided on its two end faces with a coating composed of an electrically conductive, translucent material, in order to form two electrodes 2, 3. One electrode 2 is used as the ground potential connection 4, and the other electrode 3 is provided as the high-voltage potential connection 5. The voltage which is applied between the electrodes 2, 3 is annotated V. A deflection prism 6 is arranged on that end face of the BGO crystal 1 which forms the electrode 3, while two linear polarizers (or analyzers) 9 and 10 are located on the end face of the BGO crystal 1 which forms the electrode 2, and are connected to respective collimators 7 and 8.

[0017] The polarizers 9, 10 are oriented at 45° to the axes of the crystal. They may be parallel to one another or cast through 90°.

[0018] Two light beams 11 at different wavelengths λ₁, λ₂, which are generated in a light generation unit 13, are injected into the collimator 7. These beams pass through the polarizer 9 and, polarized by the electrode 2, into the BGO crystal 1 and pass through the electrode 3, are deflected on the boundary surfaces of the deflection prism 6 and then pass through the electrode 3, BGO crystal 1, the electrode 2, the polarizer that is used as the analyzer 10, and the collimator 8. The output light beams are annotated by the number 12. They are separated in a beam splitter 14 within a detection/evaluation unit 15, and their signals are acquired and evaluated individually in the detection/evaluation unit 15. In order to evaluate the signals, the detection/evaluation unit 15 contains an evaluation means 16. Those values of the temperature T and of the electrical voltage V which solve the equation system A₁=f₁(T, V) and A₂=f₂ (T, V) are thus determined in the evaluation means 16.

[0019] If the polarizers are parallel, then the light propagation along the optical axis z for the signal strength (output power) A_(i)=A(λ_(i)) of each light beam i=1.2 after the analyzer 10 is $\begin{matrix} {{A_{i} = {A_{0,i} \cdot {\cos^{2}\left( {\frac{\pi}{2} \cdot \frac{V}{V_{h}}} \right)}}},} & (1) \end{matrix}$

[0020] where A₀, _(i) is the signal amplitude of the light beam i and V_(h) is the half-cycle voltage for the present configuration. In this case, of course, V_(h)=V_(h)(λ_(i)) should be considered as the half-cycle voltage at the wavelength λ₁. In the present case, the electric field is applied in the z direction of the crystal, and the half-cycle voltage V_(h) is given by $\begin{matrix} {{{V_{h}(\lambda)} = \frac{\lambda}{2 \cdot {r_{63}(\lambda)} \cdot {n^{3}(\lambda)}}},} & (2) \end{matrix}$

[0021] where r₆₃ is the effective electrooptical coefficient of the material for the present configuration, λ is the light wavelength of the respective light beam, and n is the refractive index of the crystal in the x or y direction.

[0022] If the polarizers are rotated at 90° with respect to one another then equation (1) is replaced by the following equation: $\begin{matrix} {A_{i} = {A_{0,i} \cdot {{\sin^{2}\left( {\frac{\pi}{2} \cdot \frac{V}{V_{h}\left( \lambda_{i} \right)}} \right)}.}}} & \left( 1^{\prime} \right) \end{matrix}$

[0023] In one preferred embodiment, a phase delay plate is inserted between the crystal and the output polarizer (analyzer) (or between the input polarizer and the crystal) and has a delay and orientation such that, when no voltage is applied, the phase difference between the two orthogonal polarizations at the output polarizer is 90°. The signal strength A_(i) is in this case given by $\begin{matrix} {A_{i} = {A_{0,i} \cdot {{\sin^{2}\left( {{\frac{\pi}{2} \cdot \frac{V}{V_{h}\left( \lambda_{i} \right)}} - \frac{\pi}{4}} \right)}.}}} & \left( 1^{*} \right) \end{matrix}$

[0024] A higher-order plate must be used for the phase delay plate to produce a delay of 90° at the two wavelengths. The advantage of using an additional phase delay plate is that it is possible to distinguish between positive and negative voltages.

[0025] In many conventional electrooptical media, the electrooptical coefficients r depend relatively strongly on the temperature T, that is to say a generally known temperature dependency

r=r(T)  (3)

[0026] exists.

[0027] In this case, the value r represents the effective electrooptical coefficient for the respective configuration, crystal symmetry and wavelength. In the above example, r=r₆₃. Both r and r(T) in general also depend on the wavelength, of course.

[0028] The equations (1), (1′) and (1*) can be described as follows in generalized form, taking into account the temperature dependency, for two light beams:

A ₁ =f ₁(V, T) and  (4a)

A ₂ =f ₂(V, T),  (4b)

[0029] where, for example in the case of crossed polarizers 9, 10, the functions f_(i) are given by $\begin{matrix} {{f_{i}\left( {V,T} \right)} = {A_{0,i} \cdot {{\sin^{2}\left( {\frac{\pi}{2} \cdot \frac{V}{V_{h}\left( {\lambda_{i},T} \right)}} \right)}.}}} & (5) \end{matrix}$

[0030] For the case of parallel polarizers, the sine must be replaced by the cosine.

[0031] Using a linear approximation, the temperature dependency of r is by, for example:

i(λ_(i) ,T)=r(λ₁ , T ₀)+K _(i) ′·ΔT,  (6)

[0032] where r(λi, T₀) is the electrooptical coefficient, which is assumed to be known, for a reference temperature T₀ and a wavelength λi, K_(I)′ is a known temperature coefficient for a wavelength λi, and ΔT=T−T₀. The precise temperature T of the electrooptical medium is generally unknown.

[0033] For the above example, the equation system (4) in the situation according to equation (1′) becomes $\begin{matrix} \begin{matrix} {{A_{1}\left( {V,T} \right)} = {\frac{A_{0,1}}{2} \cdot \left\lbrack {1 - {\cos \left( {2\quad {\pi \cdot \frac{{n^{3}\left( {\lambda_{1},T_{0}} \right)} \cdot \left( {{r_{63}\left( {\lambda_{1},T_{0}} \right)} + {{K_{1}^{\prime} \cdot \Delta}\quad T}} \right)}{\lambda_{1}} \cdot V}} \right)}} \right\rbrack}} \\ {{A_{2}\left( {V,T} \right)} = {\frac{A_{0,2}}{2} \cdot \left\lbrack {1 - {\cos \left( {2\quad {\pi \cdot \frac{{n^{3}\left( {\lambda_{2},T_{0}} \right)} \cdot \left( {{r_{63}\left( {\lambda_{2},T_{0}} \right)} + {{K_{2}^{\prime} \cdot \Delta}\quad T}} \right)}{\lambda_{2}} \cdot V}} \right)}} \right\rbrack}} \end{matrix} & (7) \end{matrix}$

[0034] The unknown parameter ΔT and hence the temperature T and the electrooptical coefficient r₆₃(T) can be calculated from the equation system (7). In this case: $\begin{matrix} \begin{matrix} {{\Delta \quad T} = {\frac{{a\quad f} - {c\quad e}}{{d\quad e} - {b\quad f}}\quad {where}}} \\ {a = {2\quad {\pi \cdot {n^{3}\left( {\lambda_{1},T_{0}} \right)} \cdot {{r_{63}\left( {\lambda_{1},T_{0}} \right)}/\lambda_{1}}}}} \\ {b = {2\quad {\pi \cdot n^{3}}{\left( {\lambda_{1},T_{0}} \right) \cdot {K_{1}^{\prime}/\lambda_{1}}}}} \\ {c = {2\quad {\pi \cdot {n^{3}\left( {\lambda_{2},T_{0}} \right)} \cdot {{r_{63}\left( {\lambda_{2},T_{0}} \right)}/\lambda_{2}}}}} \\ {d = {2\quad {\pi \cdot n^{3}}{\left( {\lambda_{2},T_{0}} \right) \cdot {K_{2}^{\prime}/\lambda_{2}}}}} \\ {e = {\arccos \left( {1 - \frac{2A_{1}}{A_{0,1}}} \right)}} \\ {f = {\arccos \left( {1 - \frac{2A_{2}}{A_{0,2}}} \right)}} \end{matrix} & (8) \end{matrix}$

[0035] Once ΔT is known, then the voltage V can be calculated directly from one of the equations (7), since: $\begin{matrix} {V = {{\arccos \left( {1 - \frac{2 \cdot A_{i}}{A_{0,i}}} \right)} \cdot {\frac{\lambda_{i}}{2\quad {\pi \cdot {n^{3}\left( {\lambda_{i},T_{0}} \right)} \cdot \left( {{r_{63}\left( {\lambda_{i},T_{0}} \right)} + {{K_{i}^{\prime} \cdot \Delta}\quad T}} \right)}}.}}} & (9) \end{matrix}$

[0036] Equation (9) has a unique solution V≦V_(h)(λ_(i)). If V>V_(h)(λ_(i)), then it is necessary to search for that solution which solves both equations (4) (or (9) for i=1 and 2).

[0037] In principle, the temperature correction for the electrooptical coefficient in accordance with equation (8) and (6) can be carried out at a considerably slower rate than the actual measurement of the voltage V. It is also possible to determine the temperature only when the respective voltage is less than the half-cycle voltage, so that the problem of an ambiguous voltage determination is irrelevant.

[0038] The temperature correction is carried out in accordance with the equation (5) or (6) using the temperature discrepancy ΔT as determined according to (8). Thanks to this measure, the electrooptical coefficients are known more accurately, so that the voltage value V can be determined with greater accuracy and reliability.

[0039] It is likewise possible for the compensation method described in (8) to be transferred to the case of parallel polarizers according to equation (1), in which case the equation system (7) and the formulae for e and f in equation (8) change in a corresponding manner.

[0040] The compensation method can also be generalized to situations in which temperature dependency of the electrooptical coefficient is not linear, as in equation (6). This may be the situation in particular in the vicinity of a phase transition of an electrooptical medium. In this situation, the appropriate functions r(T) must be inserted in the equation system (7). If necessary, the solution to the equation (7) must then be determined numerically.

[0041] Values for r(T) can be found in the literature, as well as methods for determining such values. By way of example, appropriate details for a BGO crystal can be found for various wavelengths in K. S. Lee et al., “Optical, Thermo-optic, Electro-optic and Photo-elastic Properties of Bismuth Germanate (Bi₄Ge₃O₁₂)”, National Bureau of Standards, USA 1988. Values for the temperature dependency of n³r are also given there. This combined electrooptical term n³r is referred to in the following text as R:

R=n ³ r  (10)

[0042] Since, as stated in equation (2), the half-cycle voltage V_(h) depends on R, so that A_(i) also depends on R, it is also possible to use R(T) for temperature compensation, instead of r(T). This makes it possible to achieve even better temperature compensation. The temperature dependency of r is generally considerably stronger than that of n (see, for example, the cited publication by K. S. Lee et al.) so that ignoring the temperature dependency of n, as has been stated above, results in a good approximation to the complete compensation by means of R(T).

[0043] The following formulae are obtained directly by analogy from the above equations for complete compensation, with these formulae in each case replacing those equations which have the same equation number, but without the prime:

R=R(T)=n ³(T)·r(T)  (3′)

R(λi, T)=R(λi, T ₀)+K _(i) ·ΔT  (6′)

[0044] K_(i) (without the prime) is thus the proportionality coefficients for linear temperature dependency of the combined electrooptical term R=n³r. $\begin{matrix} \begin{matrix} {{A_{1}\left( {V,T} \right)} = {\frac{A_{0,1}}{2} \cdot \left\lbrack {1 - {\cos \left( {2\quad {\pi \cdot \frac{{R^{3}\left( {\lambda_{1},T_{0}} \right)} + {{K_{1} \cdot \Delta}\quad T}}{\lambda_{1}} \cdot V}} \right)}} \right\rbrack}} \\ {{A_{2}\left( {V,T} \right)} = {\frac{A_{0,2}}{2} \cdot \left\lbrack {1 - {\cos \left( {2\quad {\pi \cdot \frac{{R^{3}\left( {\lambda_{2},T_{0}} \right)} + {{K_{2} \cdot \Delta}\quad T}}{\lambda_{2}} \cdot V}} \right)}} \right\rbrack}} \end{matrix} & \left( 7^{\prime} \right) \end{matrix}$

[0045] Determination of the temperature discrepancy: $\begin{matrix} \begin{matrix} {{\Delta \quad T} = {\frac{{a\quad f} - {c\quad e}}{{d\quad e} - {b\quad f}}\quad {where}}} \\ {a = {2\quad {\pi \cdot {{R^{3}\left( {\lambda_{1},T_{0}} \right)}/\lambda_{1}}}}} \\ {b = {2\quad {\pi \cdot {K_{1}/\lambda_{1}}}}} \\ {c = {2\quad {\pi \cdot {{R^{3}\left( {\lambda_{2},T_{0}} \right)}/\lambda_{2}}}}} \\ {d = {2\quad {\pi \cdot {K_{2}/\lambda_{2}}}}} \\ {e = {\arccos \left( {1 - \frac{2A_{1}}{A_{0,1}}} \right)}} \\ {f = {\arccos \left( {1 - \frac{2A_{2}}{A_{0,2}}} \right)}} \end{matrix} & \left( 8^{\prime} \right) \end{matrix}$

[0046] Determination of the voltage: $\begin{matrix} {V = {{\arccos \left( {1 - \frac{2 \cdot A_{i}}{A_{0,i}}} \right)} \cdot \frac{\lambda_{i}}{2\quad {\pi \cdot \left( {{R^{3}\left( {\lambda_{i},T_{0}} \right)} + {{K_{i} \cdot \Delta}\quad T}} \right)}}}} & \left( 9^{\prime} \right) \end{matrix}$

[0047] Otherwise, the same procedure as that described in the situation further above with r(T) can be used for carrying out the invention with complete compensation by means of R(T) instead of r(T). This also applies to the transferability of the equations in the situation where the polarizer 9 and the analyzer 10 are aligned parallel to one another.

[0048] A BGO crystal is used as the electrooptical medium in the above examples, with the field being applied in the z direction and the light propagation in the z direction. It is also possible to use different geometries and different electrooptical media, such as crystals composed of LiNbO₃, BSO or noncentrally polarized polymers.

[0049] The techniques described here can also be applied to the media in which the electrooptical effect is not linear (Pockel effect) but obeys a square law (Kerr effect), in which case, in particular, the equations (1), (1′), (1*), (5), (7), (7′), (8), (8′), (9) and (9′) must be adapted appropriately. Thus, for example, the sine of a square of the applied voltage must be calculated in equation (1′).

[0050] List of Reference Symbols

[0051]1: BGO crystal

[0052]2, 3: Electrodes

[0053]4: Ground potential connection

[0054]5: High-voltage potential connection

[0055]6: Deflection prism

[0056]7, 8: Collimators

[0057]9: Polarizer

[0058]10: Analyzer

[0059]11, 12: Injected and output light beams

[0060]13: Light generation unit

[0061]14: Beam splitter

[0062]15: Detection/evaluation unit

[0063]16: Evaluation means

[0064] A₀, i: Signal amplitudes

[0065] a, b, c, d, e, f: Coefficients

[0066] k: Temperature coefficient

[0067] n: Refractive index

[0068] r: Electrooptical coefficient

[0069] R: Combined electrooptical term (R=n³r)

[0070] T: Temperature

[0071] ΔT: Temperature discrepancy

[0072] V: Voltage

[0073] V_(h): Half-cycle voltage

[0074] λ₁, λ₂ Wavelengths of the injected beams 

1. A method for measurement of an electrical voltage V using an electrooptical medium (1), with the electrooptical medium (1) being subjected to an electric field which is dependent on the voltage V and with at least two polarized light beams (11) of different wavelengths (λ₁, λ₂) being injected into the electrooptical medium (1) and being polarized after the electrooptical medium (1), and with output signals AL and A₂ of the light beams being measured, where A₁ and A₂ are temperature-dependent functions f₁ and f₂ of the voltage V, characterized in that a search is carried out for those values of the temperature T and of the voltage V which solve the equation system: A ₁ =f ₁(T, V) and A ₂ =f ₂(T, V).
 2. The method as claimed in one of the preceding claims, characterized in that a voltage-induced refractive-index change in the medium (1) depends on the electric field via the Pockel effect.
 3. The method as claimed in claim 2, characterized in that the voltage dependency of the refractive-index change is described by an effective electrooptical coefficient r, with a known temperature dependency r=r(T) being assumed for the effective electrooptical coefficient r.
 4. The method as claimed in claim 2, characterized in that the voltage dependency of the refractive-index change is described by a combined electrooptical term R, with a known temperature dependency R=R(T) being assumed for the combined electrooptical term R.
 5. The method as claimed in claim 4, characterized in that a linear temperature dependency R(λi, T)=R(λ_(i), T₀)+K_(i)·ΔT where ΔT=T−T₀ with a known magnitude R(T₀) for a reference temperature T₀ and with known proportionality coefficients K_(i) is assumed for the combined electrooptical term R, with the index i=1, 2 indicating the different wavelengths (λ₁, λ₂).
 6. The method as claimed in one of the preceding claims, characterized in that the functions f₁ and f₂ depend in a non-unique way on the voltage V, and in that that voltage is determined for which both equations in the equation system are satisfied.
 7. The method as claimed in one of the preceding claims, characterized in that the electrooptical medium (1) is a crystal, in particular a BGO crystal.
 8. An apparatus for measurement of an electrical voltage V, comprising an electrooptical medium (1) which is subjected to an electric field which is dependent on the voltage V, a light generation unit (13) for generating at least two light beams (11) of different wavelengths (λ_(i), λ₂) a polarizer (9), an analyzer (10) and a detection/evaluation unit (15) for acquiring output signals AL and A₂ of the light beams (12), where A₁ and A₂ are temperature-dependent functions f₁ and f₂ of the voltage V, with the light generation unit (13), the polarizer (9) and the electrooptical medium (1) being optically connected to one another such that at least two polarized light beams (11) of different wavelengths (λ_(i), λ₂) can be injected into the electrooptical medium (1), and the electrooptical medium (1), the analyzer (10) and the detection/evaluation unit (15) are optically connected to one another such that the at least two polarized light beams (12) can be output from the electrooptical medium (1) and can be injected into the detection/evaluation unit (15), such that one of the at least two polarized light beams (11) can be polarized in the analyzer (10), characterized in that the electrooptical medium (1), the analyzer (10) and the detection/evaluation unit (15) are optically connected to one another such that also a second of the at least two polarized light beams (12) can be polarized in the analyzer (10), and in that the detection/evaluation unit (15) contains an evaluation means (16) for determination of those values of the temperature T and of the voltage V which are solutions of the equation system A ₁ =f ₁(T, V) and A ₂ =f ₂(T, V).
 9. The apparatus for measurement of an electrical voltage V as claimed in claim 8, characterized in that the electrooptical medium (1) has a voltage-induced refractive-index change which is dependent on the electric field via the Pockel effect.
 10. The apparatus for measurement of an electrical voltage V as claimed in claim 9, characterized in that, in order to determine the solution to the equation system A ₁ =f ₁(T, V) and A ₂ =f ₂(T, V), the voltage dependency of the refractive-index change can be described in the evaluation unit (15) by means of a combined electrooptical term R with a known temperature dependency R=R(T) being assumed for the combined electrooptical term R. 